Last time we introduced the tangential velocity,V, a key variable within the Formula. Today we’ll devise a new formula to compute this .tangential velocity Our starting point is the formula introduced last week to compute the amount of power,
V (1) We already know that T, and of course _{2}V, the formula for which we’ll develop today.
c, and rotational speed, _{2}N, of Pulley 2. The circumference represents the length of Pulley 2’s curved surface. The belt travels part of this distance as it makes its way from Pulley 2 back to Pulley 1. The rotational speed, _{2}N, represents the rate that it takes for Pulley 2’s curved surface to make one revolution while propelling the belt. This time period is known as the _{2}period of revolution, t, and is related to _{2}N by this equation,_{2}
t(2)_{2 } The rotational speed of Pulley 2 is specified in our example as 300 RPMs, or revolutions per minute, and we’ll denote that speed as Ninto velocity, specifically _{2 }, tangential velocityV, which is the velocity at which the belt operates, this in turn will enable us to solve equation (1). Why speak in terms of in relation to the pulley’s circumference, tangentc, as shown in the above illustration. Put another way, the belt enters and leaves the curved surface of the pulley in a straight line._{2} Generally speaking, velocity is distance traveled over a period of time, and
t(3)_{2}_{ }Since the surface of Pulley 2 is a circle, its circumference can be computed using a formula developed thousands of years ago by the Greek engineer and mathematician Archimedes. It is,
π × D(4)_{2 } where π represents the constant 3.1416. We now arrive at the formula for
t (5)_{2} Next time we’ll plug numbers into equation (5) and solve for Copyright 2017 – Philip J. O’Keefe, PE Engineering Expert Witness Blog ____________________________________ |